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Difficulty: MediumMechanics and Motion

A rescue drone with a mass of 40 kg40\text{ kg} is ascending vertically. If the drone's motors generate a constant upward lift force of 520 N520\text{ N} in an area where the acceleration due to gravity is 8 m/s28\text{ m/s}^2, what is the net upward acceleration of the drone?

  1. A
    13 m/s213\text{ m/s}^2
  2. B
    21 m/s221\text{ m/s}^2
  3. 5 m/s25\text{ m/s}^2Answer
  4. D
    0.5 m/s20.5\text{ m/s}^2

Answer

5 m/s25\text{ m/s}^2
The upward thrust of 520 N520\text{ N} is opposed by the downward gravitational force of 320 N320\text{ N} (40 kg×8 m/s240\text{ kg} \times 8\text{ m/s}^2). The resulting net upward force is 200 N200\text{ N}. Dividing this net force by the mass of 40 kg40\text{ kg} gives an upward acceleration of 5 m/s25\text{ m/s}^2.

Step-by-Step Solution

1
Calculate the downward force of gravity (weight) acting on the drone.
W=m×g=40 kg×8 m/s2=320 NW = m \times g = 40\text{ kg} \times 8\text{ m/s}^2 = 320\text{ N} downward.
Gravity exerts a constant downward force equal to the product of mass and local gravitational acceleration.
2
Determine the net vertical force acting on the drone.
Fnet=Flift−W=520 N−320 N=200 NF_{\text{net}} = F_{\text{lift}} - W = 520\text{ N} - 320\text{ N} = 200\text{ N} upward.
The upward lift and downward weight act in opposite directions along the vertical axis, so their magnitudes subtract.
3
Apply Newton's second law (Fnet=maF_{\text{net}} = ma) to solve for acceleration.
a=Fnetm=200 N40 kg=5 m/s2a = \frac{F_{\text{net}}}{m} = \frac{200\text{ N}}{40\text{ kg}} = 5\text{ m/s}^2.
Acceleration equals the net unbalanced force divided by the total mass of the object.

Key Concept

Newton's Second Law and Net Force in Vertical Motion

Alternative Method

Calculate the upward acceleration produced by the motor thrust alone (athrust=520 N40 kg=13 m/s2a_{\text{thrust}} = \frac{520\text{ N}}{40\text{ kg}} = 13\text{ m/s}^2) and subtract the downward acceleration due to gravity (8 m/s28\text{ m/s}^2), which gives 13 m/s2−8 m/s2=5 m/s213\text{ m/s}^2 - 8\text{ m/s}^2 = 5\text{ m/s}^2.
Estimated Time:1m 0s
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Topics

Mechanics and Motion

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